Why does everything Sharepoint require a trip to Google? Oh well.
If you’re trying to make a web part property editable you need two attributes, Personalizable and WebBrowsable.
You need the WebBrowsable property in order to see the property via the web interface in Sharepoint.
You need the Personalizable propetry to be able to edit it.
However, Personalizable sounds like it’s tied to an individual user (and not all users). Like many things Sharepoint it depends.
Personalizable(PersonalizationScope.Shared): Single value for all users
Personalizable(PersonalizationScope.User): Different value for all users
Credit goes to Marco Bellinaso, as I found the reference to the PersonalizationScope on his blog.